Question

2sinxcosx=sinx find general solution

Answer 1

Step-by-step explanation:

See the picture given above.Solution done.

Answer 2

Therefore the general solution of 2 sin x cos x = sin x is 'x = nπ' or 'x = 2nπ + π/3'.

Given:

The trigonometric function: 2 sin x cos x = sin x

To  Find:

The general solution of 2 sin x cos x = sin x.

Solution:

The given question can be solved as shown below.

Given trigonometric function: 2 sin x cos x = sin x

Rearranging the terms,

⇒ 2 sin x cos x = sin x

⇒ 2 sin x cos x - sin x = 0

⇒ sin x ( 2 cos x - 1 ) = 0

⇒ sin x = 0 or ( 2 cos x - 1 ) = 0

Case-1:

⇒ sin x = 0

The general solution of sin x = 0 is 'x = nπ'.

Case-2:

⇒ 2 cos x - 1 = 0

⇒ 2 cos x = 1

⇒ cos x = 1/2

The general solution of 2 cos x - 1 = 0 is 'x = 2nπ + π/3'

Therefore the general solution of 2 sin x cos x = sin x is 'x = nπ' or x = 2nπ + π/3'.

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